Viscoelastic materials Alfrey (1957) listed 3 methods that use experimental curves to map out the viscoelastic character of a material: Creep curve: function of time Ralaxation curve: function of time Dynamic modulus curve: dynamic modulus as a function of frequency of the sinusoidal strain All of them should be independent of the magnitude of the imposed stress or strain. (linear viscoelastic materials)

Dynamic tests

Dynamic testing Rapid test with minimal chemical and physical changes. There are 4 types (Morrow and Mohsenin, 1968): Direct measurement of stress and strain Resonance methods Wave propagation methods Transducer methods

Dynamic tests There are 3 criteria for dynamic tests L/ < 1 : direct measurement of sinusoidally varying  and  (use in most foods) L/ = 1 : resonance vibration L/ > 1 : pulsed wave propagation (ultrasonic, sound wave: high frequency or low ) L = length of sample  = wave length

direct measurement of sinusoidally varying  and  Dynamic-Mechanical Analysis (DMA) direct measurement of sinusoidally varying  and 

Dynamic or oscillatory tests Dynamic or oscillatory tests are performed to study the viscoelastic properties of a sample. The tests are called microscale experiments compared to macroscale tests like rotational or viscometry tests. Viscoelastic samples have both elastic (solid) and viscous (liquid) properties, the extreme described by Hooke’s law of elasticity and Newton’s law of viscosity.

Parallel-plate geometry for shearing of viscous materials (DSR instrument). Rheometrics RFS II

Dynamic mechanical analysis (DMA), dynamic mechanical thermal analysis (DMTA) or dynamic thermomechanical analysis is a technique used to study and characterize materials. It is most useful for observing the viscoelastic nature of polymers. An oscillating force is applied to a sample of material and the resulting displacement of the sample is measured. From this the stiffness of the sample can be determined, and the sample modulus can be calculated. By measuring the time lag in the displacement compared to the applied force it is possible to determine the damping properties of the material.

Viscoelastic materials such as polymers typically exist in two distinct states. They exhibit the properties of a glass (high modulus) at low temperatures and those of a rubber (low modulus) at higher temperatures. By scanning the temperature during a DMA experiment this change of state, the glass transition or alpha relaxation, can be observed.

Dynamic Mechanical Testing Deformation An oscillatory (sinusoidal) deformation (stress or strain) is applied to a sample. The material response (strain or stress) is measured. The phase angle , or phase shift, between the deformation and response is measured. Response Phase angle d

Dynamic Mechanical Testing: Response for Classical Extremes Purely Viscous Response (Newtonian Liquid) Purely Elastic Response (Hookean Solid)  = 90°  = 0° Stress Stress Strain Strain

Dynamic Mechanical Testing: Viscoelastic Material Response Phase angle 0° < d < 90° Strain Stress

Dynamic (Oscillatory) Rheometry The ideal elastic solid A rigid solid incapable of viscous dissipation of energy follows Hooke’s Law, wherein stress and strain are proportional (s=Ee). Therefore, the imposed strain function: e(w)=eo sin(wt) generates the stress response (w)=E eosin(wt) =  o sin(wt) and the phase angle, d, equals zero. Where eo = maximum amplitude  = 2¶f = angular frequency f = frequency in Hz or cycle/s

Dynamic (Oscillatory) Rheometry B. The ideal viscous liquid A viscous liquid is incapable of storing inputted energy, the result being that the stress is 90 degrees out of phase with the strain. An input of: e(w)=eo sin(wt) generates the stress response (w)=  o sin(wt+p/2) and the phase angle, d, p/2. Where eo = maximum amplitude  = 2¶f = angular frequency f = frequency in Hz or cycle/s

DMA Viscoelastic Parameters: The Complex, Elastic, & Viscous Stress The stress in a dynamic experiment is referred to as the complex stress * The complex stress can be separated into two components: 1) An elastic stress in phase with the strain. ' = *cos ' is the degree to which material behaves like an elastic solid. 2) A viscous stress in phase with the strain rate. " = *sin " is the degree to which material behaves like an ideal liquid. Phase angle d Complex Stress, * * = ' + i" Strain, 

Generally, measurements for visco Generally, measurements for visco. materials are represented as a complex modulus E* to capture both viscous and elastic behavior: E* = E’ + iE” E*2 = E’2 + E”2

In dynamic mechanical analysis (DMA, aka oscillatory shear or viscometry), a sinusoidal  or  applied. 0 = peak stress E’ = 0 cos/0 = E* cos E” = 0 sin/0 = E* sin

Schematic of stress  as a function of t with dynamic (sinusoidal) loading (strain).

The “E”s (Young’s moduli) can all be replaced with “G”s (rigidity or shear moduli), when appropriate. Therefore: G* = G’ + iG" where the shearing stress is  and the deformation (strain) is  or . Theory SAME.

Complex modulus - G* The complex modulus describes the total resistance of the sample to oscillatory shear, s = G* g Similar is he resistance to flow in rotational tests, . s = h g The complex modulus is determined in an oscillatory test at small angles of deformation. The viscosity is, on the other hand, calculated in rotational tests at varying shear rates (large deformation rates)

In analyzing polymeric materials: G* = (0)/(0), ~ total stiffness. In-phase component of IG*I = shear storage modulus G‘ ~ elastic portion of input energy = G*cos

The out-of-phase component, G" represents the viscous component of G The out-of-phase component, G" represents the viscous component of G*, the loss of useful mechanical energy as heat = G*sin = loss modulus The complex dynamic shear viscosity * is G*/, while the dynamic viscosity is  = G"/ or  = G"/2f

For purely elastic materials, the phase angle  = 0, for purely viscous materials, 90. The tan() is an important parameter for describing the viscoelastic properties; it is the ratio of the loss to storage moduli: tan  = G"/ G',

G* = G’+iG’’= (G’2+G’’2)1/2 Complex modulus G* G* = G’+iG’’= (G’2+G’’2)1/2 tan  = G” / G’ G’’ G* G’ = elastic modulus or storage modulus G’’ = viscosity modulus or loss modulus tan  = phase angle or loss angle d G’

Tests Dynamic Oscillatory Shear Test Plate oscillates at increasing frequencies Strain and stress are measured to determine G’ and G’’ G’ represents the elastic (storage) modulus G’’ represents the viscous (loss) modulus When G’ > G’’ the fluid behaves more elastic When G’ < G’’ the fluid behaves more viscous

Phase angle - tan d = damping factor Phase angle tan d is associated with the degree of viscoelsticity of the sample. A low value in tan d or d indicates a higher degree of viscoelasticity (more solidlike). The phase angle d can be used to describe the properties of a sample. d = 90  G*= G´´ and G´= 0  viscous sample d = 0  G*= G´ and G´´= 0  elastic sample 0 < d < 90   viscoelastic sample d > 45   G´´> G´  semi liquid sample d < 45   G´> G´´  semi solid sample

Complex viscosity - h* Complex viscosity describes the flow resistance of the sample in the structured state, originating as viscous or elastic flow resistance to the oscillating movement. h* = G* / w w = 2pf A high value for the complex viscosity the greater is the resistance to flow in the structured state.

DMA Viscoelastic Parameters The Modulus: Measure of materials overall resistance to deformation. G = Stress/Strain The Elastic (Storage) Modulus: Measure of elasticity of material. The ability of the material to store energy. G' = (stress/strain)cos The Viscous (loss) Modulus: The ability of the material to dissipate energy. Energy lost as heat. G" = (stress/strain)sin Tan Delta: Measure of material damping - such as vibration or sound damping. Tan = G"/G'

of a Viscoelastic Material Storage and Loss of a Viscoelastic Material SUPER BALL LOSS TENNIS BALL X STORAGE

DMA Viscoelastic Parameters: Damping, tan  Dynamic measurement represented as a vector G" Phase angle  G' The tangent of the phase angle is the ratio of the loss modulus to the storage modulus. tan  = G"/G' "TAN DELTA" (tan ) is a measure of the damping ability of the material (damping properties).

Viscoelasticity in Crosslinked, Amorphous Polymers Plots of log G’, log G” and tan against log angular frequency (in radians per second) for a typical elastomer above its Tg; Poly(styrene-co-butadiene) lightly vulcanized with a peroxide cure. Note that at low frequencies the material has a low modulus and behaves elastically. As frequency is increased, the material becomes stiffer, and less capable of storing inputted energy (generates heat upon deformation). Storage modulus Loss modulus tan  = G” / G’

Other methods L/ = 1

Resonance Vibration Method In physics, resonance is the tendency of a system to oscillate at maximum amplitude at a certain frequency. This frequency is known as the system's natural frequency of vibration, resonant frequency, or eigenfrequency.

1 0.5 w0.5 Wr = frequency at ratio equal to 1.0 Amplitude ratio

Free vibration method Make an object vibrate freely. Vibration will stop with time. Due to internal friction or viscosity, the dead of amplitude after time occurs. Force acts here A1 A2

L/ > 1

The use of ultrasonic or sound wave for properties determination Pulse Method: Pulse = short duration wave (discontinuous) Ultrasonic: high frequency Transducer will produce ultrasonic wave. Input and output data can be obtained. Time for sound travel through specimen can be calculate from length by time (L/T=velocity).

Determination of water content in crude oil

Instrument Test cell amplifier Pulse generator oscilloscope receiver transducer